The Inertia Tensor Versus Static Moment and Mass in Perceiving Length and Heaviness of Hand-Wielded Rods

In 2 experiments, participants haptically estimated length and heaviness of handheld rods while wielding without seeing them. The sets of rods had been constructed such that variation of static moment and the 1st eigenvalue of the inertia tensor (I 1) were separated. Consistent with previous findings, perceived rod length correlated strongly with I1. However, multiple regressions on current data as well as data from previous studies showed a comparable strong correlation between perceived rod length and static moment plus mass. Contrary to previous findings, perceived heaviness correlated strongly with static moment and only weakly with the eigenvalues of the inertia tensor. These results suggest that the inertia tensor does not provide the sole foundation for a theory of dynamic touch. In the past decade or so, significant strides have been made in understanding the perception of properties of objects that are held in the hand but not seen. A large body of experimental data has been presented in support of the hypothesis that many instances of haptic perception are governed by a single yet multivalued physical entity, the inertia tensor ( I). This 3 3 tensor is symmetrical and thus contains six independent numbers. In diagonalized form—that is, when the tensor is expressed with respect to the unique set of axes of symmetrical mass distribution (the so-called principal axes of inertia)—the inertia tensor consists of three elements denoted as the principal moments of inertia or eigenvalues. These principal moments define an object’s (invariant) resistance against rotational acceleration around its principal axes of inertia and have been found to be related to perception of an object’s length (Solomon & Turvey, 1988; Solomon, Turvey, & Burton, 1989a, 1989b), width and height (Turvey, Burton, Amazeen, Butwill, & Carello, 1998), and heaviness (Amazeen & Turvey, 1996). In addition, the eigenvectors of the inertia tensor (defining the direction of the principal axes of inertia of the object) have been found to be related to the perception of an object’s orientation (Pagano & Turvey, 1998; Turvey, Burton, Pagano, Solomon, & Runeson, 1992). More recently, it has been suggested that perception of grip position is a function of the off-diagonal elements of the inertia tensor (i.e., the products of inertia; Pagano, KinsellaShaw, Cassidy, & Turvey, 1994) and that the perception of an object’s partial forward length (i.e., the distance from the hand to the forward-directed endpoint of the rod) is a function of both the moments and products of inertia (Carello, Santana, & Burton, 1996; Pagano, Carello, & Turvey, 1996). In the majority of the studies cited, the invariance of I as well as the fact that it provides information about both magnitude and direction, has been emphasized to support the inertia tensor hypothesis. However, when an object is held as still as possible, it appears difficult to perceive its properties through I because, by definition, an object’s resistance to rotation manifests itself only when the object is rotated. Under static conditions, physical properties such as the static moment (i.e., the first moment of mass